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Statistical Analysis of Current Win Rates

The Ecdysiast··5 votes·2,970 views

The win rates I used to calculate these came from Lolking. Generally, sites like this will have the overall average win rate, but lack the Standard Deviation to make it actually mean something. It bothered me that no site actually has this information, so I did the calculations myself.

The current average win rate is 49.6%, with a Standard Deviation of 2.8%.

17 Champions are more than 1 Standard Deviation below the mean. (But not 2 Stdevs below)

  • These champions have a win rate between 46.8% and 44%, making them weaker than 80.4% of all champions: Akali, Alistar, Bard, Cho'gath, Elise, Evelynne, Gragas, Kindred, LeBlanc, Lissandra, Lucian, Rek'sai, Shen, Taliyah, Viktor, Vladimir, Zed

16 Champions are more than 1 Standard Deviation above the mean. (But not 2 Stdevs above)

  • These champions have a win rate between 52.4% and 55.2%, making them stronger than 85.8% of all champions: Amumu, Blitzcrank, Brand, Fiddlesticks, Galio, Janna, Rammus, Shaco, Taric, Teemo, Vel'koz, Vi, Wu Kong, Yorick, Ziggs, Zyra

The following champions are very weak Overall, with win rates more than 2 Standard Deviations below the mean: Azir 42.2% (only 1% from being 3 Stdevs below) Nidalee 42.5% Ryze 43.4% --overall. See footnote. Nunu 43.8%

The following champions are very strong Overall, with win rates more than 2 Standard Deviations above the mean: Swain 55.4% Sona 56.4% KogMaw 57.6% (only 0.4% from being 3 Stdevs above) ######There were no champions found to have win rates 3 Standard Deviations below or above the mean. Do note that win rates based on skill level serve to show that champion balance is being ignored due to massive outliers in both directions from the mean. Ryze, for example, has a win rate 7 stdevs above the mean for Diamond+, which is insane to say the least.

Side Notes:

  1. There are currently 40 Unbalanced champions (above or below 1stdev), for a total of 94 Balanced ones. This means that 70.1% of champions in the game are currently balanced.
  2. There are currently 19 "Overpowered" champions (above 1stdev), for a total of 115 that are either balanced or weak. This means that 85.8% of champions are not overpowered, and 14.2% of champions are overpowered.
  3. Not a single one of the most popular champions this month were 2 Standard Deviations above the mean. Which means that their high pick rate only serves to verify that each of those champions is in fact balanced.
  4. Oddly enough, Kog'maw is the 4th Least Popular champion. Nunu is 3rd Least Popular. However, several others share the same percentage for popularity despite slightly higher number of games played.

Conclusions: Azir, Nidalee, Ryze, and Nunu have win rates significantly low enough to need buffs. Though I hope for a complete re-release in Nunu's case. Swain, Sona, and Kog'maw have win rates significantly high enough to need nerfs.

However, the distribution of these win rates is cause for concern. Champions with winrates that are only near 50% because low-skill players win 30% and high-skill players win 70% means that such champions are too difficult for an incredibly large majority of players, which is not healthy. Riot's obligations are not to make the highest-skill players able to abuse champions for 70% chance to win, their obligations are to make champions that are reasonably fair for everyone.

Ryze and Sona are such examples. Ryze's win rate is artificially high because the highest skill players win an incredibly amount with him. On the other side of it, Sona's is artificially high because lower skilled players don't know how to play against her.

Champions such as these who show "balanced" win rates across the board due to extreme outliers in both directions are too often weakened in favor of the highest 2% of players rather than adjusted fairly for everyone.

I was very surprised by the numbers I found. The average player would assume that the "OP" champions everyone complains about would have higher win rates, but the numbers show otherwise. It sure is something to think about, that Vayne, Riven, Fizz, Yasuo, Yi, Teemo and other "toxic" champions aren't currently strong.

Do keep in mind that pick rates and number of games played have a strong impact on whether or not a champion needs to be adjusted. One strong example is Taliyah, whose win rate is about 8-9 stdevs away from the mean of 49.6% win rate for any player who hasn't played at least 150 games with her. Game length also plays a factor, but whether or not a champion is actually able to reach the point in the game where they have 49.6% win rate decides if that champion needs early-game buffs.

Here "stronger" is defined as more likely to win, and "weaker" is defined as less likely to win.

35 Comments

Ahristocats3 votes

{quoted}

Swain and Sona need nerfs

i would have seen everything with this

BluePolarizer3 votes

Ryze can't be buffed because in the hands of OTPs, he is essentially unstoppable. If you look at http://champion.gg/champion/Ryze you'll find that Ryze has a 90% win rate on ppl who play 125+ ranked games of Ryze. In addition he is a heavily contested pick in competitive, with Faker logging a 72% win rate on Ryze in Korean challenger after only 18 games: http://www.op.gg/summoner/userName=hide+on+bush

The Ecdysiast1 votes

Then it looks like they'll have to lower the skill cap and add nerfs, instead of adding buffs.

Strictly speaking, it doesn't matter what the top 0.5% of players do. This is a company that makes most of its profit from its casual players. Their obligation is to make the game balanced for the majority regardless of what the smallest possible group of players is doing to abuse their designs.

But I did address this phenomenon briefly near the end, with the similar example of Taliyah. There's not much to be done about champions that experienced players can abuse to drastically increase their odds of winning.

LankPants3 votes

The current average win rate is 49.6%

This alone shows why LoLking is an abysmal stat sight. The average winrate of all champions inherently has to be 50%. Whenever one champ wins, another loses, so your sample has to average out to 50%. The fact that LoLkings do not, as well as the fact that even its internal statistics don't add up show that it's a joke of a stat site.

If you want an accurate stat site look at Lolaytics or op.gg , their stats are far more accurate.

Michael Sykes1 votes

{quoted}

This alone shows why LoLking is an abysmal stat sight. The average winrate of all champions inherently has to be 50%. Whenever one champ wins, another loses, so your sample has to average out to 50%. The fact that LoLkings do not, as well as the fact that even its internal statistics don't add up show that it's a joke of a stat site.

If you want an accurate stat site look at Lolaytics or op.gg , their stats are far more accurate.

Lolalytics is actually the best site atm and way underrated. It even does have stats for any gamemode.

The Ecdysiast1 votes

Do either of those sites also include the standard deviation for me so I don't have to do it?

If not, they're jokes as well.

However, some champions were given stats for several roles, which could account for the value slightly lower than 50% that we see.

I like your name though.

Omen462 votes

interesting but not surprising, It is easy to believe that statistic, the less popular champions have powerful abilities still, and the ones that are op are probably picked by new players and players looking only to get easy wins. I can't tell you how many times many of your list of 'op' champs have 1v5 teams and walked away full hp. exception of Teemo Yasuo. Generally popular champions will have lower win rates due to the fact that not just good players but REALLY bad players play them. btw if you could do me a favor, I would love to know the statistics on 2 very special champions in my heart, <GnarKindred3

The Ecdysiast1 votes

I can partially answer that without even looking at my numbers again. Gnar and Kindred have a 0.7% and 0.6% pick rate respectively-- a percentage on par with the top 10 least popular champions. That's because the use of percentages means there can be a difference of thousands of games within the same percentage range.

I edited the post to include the names of the champions between 1 and 2 standard deviations from the mean, probably while you were reading the post and typing your response.

Kindred falls into the "between 1 SD and 2 SD's below the mean" category. So she is in need of some minor buffs. Gnar is actually 0.1% away from falling into that category as well. So both are relatively weak at the moment.

Omen461 votes

well appreciated but it makes me sad, I have such a fantastic love of this 'Mr. Hyde' and 'lady and sir death'

Quepha1 votes

Ryze is really strong in pro play. Azir has been seen in pro play indicating that he is either strong again or right on the line, Nidalee in the past has been shown to be a champion that gets to be incredibly strong in pro play long before she gets a good solo queue winrate.

Frozne2 votes

{quoted}

Ryze is really strong in pro play. Azir has been seen in pro play indicating that he is either strong again or right on the line, Nidalee in the past has been shown to be a champion that gets to be incredibly strong in pro play long before she gets a good solo queue winrate.

he's not strong at all lmao theres a reason hes been picked 3 times and of the 3 times picked in na lcs he hasnt won a game

The Ecdysiast1 votes

Regardless, these statistics are for overall play.

And statistically speaking, a group far below 1% of players is not a big enough group to gather data from. It doesn't matter if the best players can abuse a champion. Riot's obligations are to the majority, not the extreme-elite.

Michael Sykes1 votes

{quoted}

Regardless, these statistics are for overall play.

And statistically speaking, a group far below 1% of players is not a big enough group to gather data from. It doesn't matter if the best players can abuse a champion. Riot's obligations are to the majority, not the extreme-elite.

Actually this is not true - they try to balance both for high and low Elo, which has been proved by the most recent Ryze nerfs. Additionally, some champions you mentioned which are on the weaker side have very high Winrates in Plat+, where the average player can learn many high Skill cap champions faster

Quepha1 votes

{quoted}

Riot's obligations are to the majority, not the extreme-elite.

That's simply not true if you look at the history and origins of this game. League of Legends was founded on the idea that the team would focus on making the game competitive and listen to feedback from the highest tier of players. The lasting appeal of League of Legends comes from the knowledge players have that an extremely elite sphere of players exists who play the game professionally and appreciate the depth of the game in that environment. Casual players matter too, but Riot has to respect all levels of play and make sure that competitive League of Legends is a fun and attractive environment.

The Ecdysiast1 votes

Their obligations are to the largest group of players that give them money.

Regardless of what they've claimed, which is often lies anyway, they are a company. If they cannot make the game reasonably fun for players that aren't professional, they are failing.

Craft Zeppelin1 votes

I cant help but notice the majority of void champions having low playrates/high winrates at all times of the season. And most of them are soloque stompers that makes near surgical levels of disruptions to the instability of the game.

The Ecdysiast2 votes

This is clearly intentional, and plays into the lore. k a p p a

Kaioko1 votes

Like you said -- pick rate makes all the difference and essentially renders the analysis unreliable on its own to be used for decision making.

The Ecdysiast1 votes

In some cases pick rate is determined by champion weakness. Such is the case with Nunu and Azir.

There are a ton of other factors to consider to determine whether a champion is going to be balanced, but from what we've seen on nearly every new champion release, Riot simply has the New Champion team designing with little actual calculation done.

It would be a simple week's task to find the statistics for the amounts of defenses, DPS, CC time, Resource cost, etc. and apply those to the base values and scalings of new champions. Either they haven't done that yet, or as I heavily suspect, they definitely have, and intentionally abuse these calculations in order to make new releases so strong that people would be willing to purchase them for Riot Points.

chipndip11 votes

League of Graphs has Sona's Diamond win rate back at 49%. Can we fucking stop with this shit?

The Ecdysiast1 votes

Which doesn't matter. That means that less than 2% of players have Sona within 1stdev of the mean win rate. That's not a reasonable amount of players.

Champions who are balanced at higher levels of play, or extremely overpowered at high levels of play and extremely weak at low levels are inherently unbalanced for the game as a whole.

You can argue the meaning of the statistics, but you can't ignore what they mean for the game as a whole vs. the game for an incredibly small minority of players.

chipndip11 votes

Or you balance champs for lower levels of play so they're actually worthless when you finally understand how to play the game at all...like Garen.

Sona doesn't need nerfs more than she needs a redesign. Regardless, she isn't broken. LoG has her gold win rate at like...52% anyway. Where is this 57% coming from? The wind!?

zarxus12341 votes

all we have to say is ryze... to invalidate this post.

The Ecdysiast1 votes

Read the whole post then.

There is nothing invalid about the numbers.

However, if Riot considers Ryze balanced based on massive outliers, then that is where the problem lies. As I've addressed in the post.

WoonStruck1 votes

Should find a correlation between winrate and play rate and standard deviation.

dim2a1 votes

You are greatly misusing statistics here.

"There are currently 40 Unbalanced champions (above or below 1stdev), for a total of 94 Balanced ones."

Suppose for a second that the game was perfectly balanced, and each champion's expected winrate was 50%. How many champions would be "unblanced" by your measure on average? 134 * . 32 ~= 42, which is very close to the current 40, champions would be 1 stdev away from 50% winrate due to random chance in a perfectly balanced game.

What it tells me is that your analysis does NOT show the game is unbalanced in any form, in fact it is very close to what we expect in a perfectly balanced game. Now it does not mean the game is perfectly balanced, in fact correct application of statistics will show some unbalanced champions. But the method you are using is incorrect, as it would indictate pretty much the imblanace you show in a perfectly balanced game, on average.

The Ecdysiast1 votes

Your definition of perfect balance is where we differ.

Perfect balance is not a the Normal model. Perfect balance would be a 50% win rate for every champion with a standard deviation of 0.

Yes, we expect to see numbers like this from the normal model. No, that does not mean that the game's ability to reflect Normality is the same as balance.

If there are champions that need to be banned due to an oddly high probability of winning, then that is not the goal of balance. The ban phase is meant to counter the team you want to use, not simply lock out the high outliers from normality.

The analysis shows that the game is in fact unbalanced, but that the unbalance we see is what is to be expected. Meeting expectations does not, however, mean that things are just.

Quepha1 votes

{quoted}

Your definition of perfect balance is where we differ.

Perfect balance is not a the Normal model. Perfect balance would be a 50% win rate for every champion with a standard deviation of 0.

Ideal balance for Lee Sin would have his winrate below 50% because a bunch of people play him without knowing what they're doing. The only way to avoid the Lee Sindrome winrate tax is to make every champion play exactly the same with no variety.

The Ecdysiast1 votes

Lee Sin isn't actually an example for the phenomenon you're describing.

  1. His win rate is below 50%. It's 47.5%.
  2. His win rate by games played is a strange curve, but does not go above 50% even as games played increases to "main" levels.

I don't see why you're so fixated on Lee Sin, since he's relatively balanced.

You kinda dug yourself a whole with that "only way" thing. There's always many ways to do things. As we've seen from Riot, they found a way to nerf Xin by lowering his healing and E, without reverting the guaranteed crit that was obviously the issue when they added it.

For high skillcap cases, Itemization could be fixed to accommodate different levels of skill. For example, I choose to build Ezreal with a full critical strike chance build since I don't trust my ability to land every Q (or my enemy's ability to stand completely still so I can do so). This works for me, but likely would not stand at diamond levels of play.

Quepha1 votes

{quoted}

Lee Sin isn't actually an example for the phenomenon you're describing.

  1. His win rate is below 50%. It's 47.5%.
  2. His win rate by games played is a strange curve, but does not go above 50% even as games played increases to "main" levels.

I don't see why you're so fixated on Lee Sin, since he's relatively balanced.

You kinda dug yourself a whole with that "only way" thing. There's always many ways to do things. As we've seen from Riot, they found a way to nerf Xin by lowering his healing and E, without reverting the guaranteed crit that was obviously the issue when they added it.

For high skillcap cases, Itemization could be fixed to accommodate different levels of skill. For example, I choose to build Ezreal with a full critical strike chance build since I don't trust my ability to land every Q (or my enemy's ability to stand completely still so I can do so). This works for me, but likely would not stand at diamond levels of play.

You said ideal balance would be if every champion was at 50% winrate.

Lee Sin is below 50% winrate and you say he is balanced.

Crit build Ez sucks, there are tons of champions you would pick over him with that build. If his winrate was the same as those other champions with that build, then his winrate with a build that actually complements his kit would be much better.

The Ecdysiast1 votes

Yeah... it seems you don't know anything about stats even with all of the information handed to you. You're just padding your comments with nonsense that contradicts the numbers I very plainly stated for you. There's nothing I can do about ignorance.

SNSD Sunnny1 votes

Correct statistical methods can confirm this game is anything but balanced.

If the game was perfectly balanced, every champion has a true win rate of 50%. Each champion has over 100k games played in the last year. Variance of 50% win rate is 25% in a single game. The variance over 100k games would be .0000025. This means the 1 standard deviation range of a balanced champion is around 48.5% to 51.5%. However, that's not taking into account that the game is a 5 v 5 game, not a 1 v 1 game. The true range of balance would be much lower, like 49.7% to 50.3%.

People don't understand how insanely unbalanced a 55% win rate champion is, it means you are at 5 to 4 odds to win the game in a 5 v 5 game, not even a 1 v 1 game. A 5 v 5 game also lowers the variance even farther. Top challengers only hold around a 55% to 60% win rate. A champion with a 55% win rate literally has 0 counter picks since the champion probably wins lane 100% of the time, or is useful even when losing lane. Even a 1% advantage would be huge with such a large sample size and the fact that it's a 5 v 5 game.

Anybody who wins 55% at the top level is considered a god already.

dim2a1 votes

[{quoted}](name=SNSD Sunnny,realm=NA,application-id=3ErqAdtq,discussion-id=VEnGvRWE,comment-id=000a0001,timestamp=2017-01-25T20:36:45.661+0000)

Correct statistical methods can confirm this game is anything but balanced.

yes, this is what I pretty much said at the end, BUT my point is that OP's statistical methods are not correct and would show ANY game to be imbalanced, with high probability.

The Ecdysiast1 votes

My methods were correct. Don't blame me for Lolking's mistakes.

I also already pointed out that the existence of different-role winrates on several champions can account for the slight difference from the true mean. You can do me a favor and do the h-test for whether or not 0.4% is statistically significant for 50% being the true mean.

NodirjonSattarov1 votes

Did you take into consideration the play rate for Kog'Maw? He hasn't been touched since patch 6.24 which was 2 months ago and barely has a 1% play rate. So you're concluding to nerf a champion that has little to no play in a meta that is supposed to obliterate him (he has no CC or disengage). ok

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